3a^2=12+9a

Solution for 3a^2=12+9a equation:

Simplifying
3a2 = 12 + 9a

Solving
3a2 = 12 + 9a

Solving for variable 'a'.

Reorder the terms:
-12 + -9a + 3a2 = 12 + 9a + -12 + -9a

Reorder the terms:
-12 + -9a + 3a2 = 12 + -12 + 9a + -9a

Combine like terms: 12 + -12 = 0
-12 + -9a + 3a2 = 0 + 9a + -9a
-12 + -9a + 3a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
-12 + -9a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -3a + a2) = 0

Factor a trinomial.
3((-1 + -1a)(4 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -1a)' equal to zero and attempt to solve:

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -1a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1a = 0 + 1
-1a = 0 + 1

Combine like terms: 0 + 1 = 1
-1a = 1

Divide each side by '-1'.
a = -1

Simplifying
a = -1
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-1, 4}